1 条题解

  • 0
    @ 2022-6-5 10:44:06

    luogu

    #include <bits/stdc++.h>
    
    using pii = std::pair<int,int>;
    const int inf = 1e7;
    
    int dx[] = {0,1,0,-1};
    int dy[] = {1,0,-1,0};
    
    int n,m,dis[12][12],ban[12][12];
    
    std::map< std::vector<int> , int >dp[12][12];	
    
    std::vector<int> process(std::vector<int>S) {
    	int cnt = 1;
    	int vis[30] = {0};
    	for (int i = 1; i <= n + 1; ++ i) {
    		if (S[i] == 0 || S[i] == 1) continue;
    		if (!vis[S[i]]) { vis[S[i]] = ++cnt; S[i] = cnt; }
    		else S[i] = vis[S[i]];
    	} return S;
    }
    std::vector<int> shift(std::vector<int>S){ for (int i = 1; i <= n; ++ i) S[i] = S[i+1]; S[n+1] = 0; return S; }
    std::vector<int> trans(std::vector<int>S,int i) { std::swap(S[i],S[i+1]); return S; }
    std::vector<int> create(std::vector<int>S,int i) { S[i] = S[i+1] = 20; return process(S); }
    std::vector<int> merge(std::vector<int>S,int i) {
    	int p = S[i], q = S[i+1], flag = 20;
    	if (p == 1 || q == 1) flag = 1;
    	for (int i = 1; i <= n + 1; ++ i) if (S[i] == p || S[i] == q) S[i] = flag;
    	S[i] = S[i+1] = 0;
    	return process(S);
    }
    
    int main() {
    	
    	scanf("%d%d",&n,&m);
    	for (int i = 1; i <= m; ++ i) {
    		int x,y;
    		scanf("%d%d",&x,&y);
    		ban[x][y] = 1;
    		assert( not ( (x == 1 && y == n)  or (x == n && y == 1) ) );
    	}
    	
    	auto bfs = [&]() {
    		std::memset(dis,-1,sizeof(dis));
    		std::queue< pii >q;
    		q.push( { 1,n } );
    		dis[1][n] = 0;
    		while (q.size()) {
    			auto u = q.front(); q.pop();
    			int x = u.first, y = u.second;
    			for (int i = 0; i < 4; ++ i) {
    				int x1 = x + dx[i], y1 = y + dy[i];
    				if (x1 < 1 || x1 > n || y1 < 1 || y1 > n || dis[x1][y1] != -1 || ban[x1][y1]) continue;
    				dis[x1][y1] = dis[x][y] + 1;
    				q.push( { x1,y1 } );
    			}
    		} 
    	};  bfs();
    	
    	std::vector<int>v(n+2);
    	v[n+1] = 1; dp[1][n-1][v] = 1;
    	v[n+1] = 0; v[n] = 1; dp[1][n-1][v] = 1;
    	
    	for (int i = 1; i <= n; ++ i) {
    		for (int j = n - (i == 1); j >= 1; j --) {
    			for (auto P:dp[i][j]) {
    				auto S = P.first; int v = P.second;
    				int p = S[j], q = S[j+1];
    				if (p == 0 && q == 0) dp[i][j-1][S] = std::max(dp[i][j-1][S],v);
    				if (ban[i][j]) continue;
    				if (p == 0 && q == 0) {
    					auto T = create(S,j);
    					dp[i][j-1][T] = std::max(dp[i][j-1][T],v + 1);
    				}
    				if ((p != 0) + (q != 0) == 1) {
    					dp[i][j-1][S] = std::max(dp[i][j-1][S],v + 1);
    					auto T = trans(S,j);
    					dp[i][j-1][T] = std::max(dp[i][j-1][T],v + 1);
    				}
    				if (p && q && p != q) {
    					auto T = merge(S,j);
    					dp[i][j-1][T] = std::max(dp[i][j-1][T],v + 1);
    				}
    			}
    		} for (auto P:dp[i][0]) {
    			auto S = P.first; int v = P.second;
    			if (S[1] == 0) dp[i+1][n][shift(S)] = dp[i][0][S];
    		}
    	}
    	std::vector<int>S1(n+2),S2(n+2);
    	S1[1] = 1; S2[2] = 1;
    	printf("%d",std::max(dp[n][1][S1],dp[n][1][S2]) - dis[n][1]);
    	return 0;
    }
    
    • 1

    信息

    ID
    686
    时间
    1000ms
    内存
    512MiB
    难度
    7
    标签
    递交数
    5
    已通过
    5
    上传者